Low interest rates have pushed down stock yields, but declining rates are nothing new.

In fact, rates have been slowly declining since peaking in the early 1980s.

But this decline has made finding reliable high-yield dividend stocks difficult.

There are simply too many investors clamoring to get into too few high-yielding securities. This pushes up stock prices and pushes down yields.

The three stocks combine high yields with consistency, boasting 7%-plus dividend yields and 10-plus consecutive years of dividend increases.

All three are Dividend Achievers, a select group of 274 stocks with 10 or more consecutive years of dividend increases. 

1. Alliance Resource Partners  (ARLP - Get Report)
This master limited partnership operates in the coal industry. It goes without saying that the past year hasn't been kind to coal mining companies.

Although the stock has nearly doubled from its 52-week low, it is still down nearly 20% this year. And, due to the steep decline in coal demand in the U.S., Alliance Resource Partners cut its distribution by 35% this year.

Prior to the distribution cut, Alliance Resource Partners had a tremendous streak going, of 29 consecutive quarterly distribution increases.

Alliance Resource Partners has its share of challenges, namely the drop in coal sales due to increasing regulatory scrutiny of coal and low natural-gas prices, which has compelled utilities to switch to natural gas instead of using coal.

These headwinds caused the MLP's revenue and earnings per unit to decline 27% and 30%, respectively, over the first half.

That being said, Alliance Resource Partner still has an 8.5% yield even after the cut, which is still a very high yield. And, the company enjoys significant operational advantages that set it apart from the rest of the coal industry.

First, Alliance Resource Partners has significant scale, thanks to its geographic focus. Its coal mines are positioned near its end users and industrial customers, which lowers production and transportation costs.

In addition, the company focuses on thermal coal from the Illinois Basin, which has stronger economics than coal from other parts of the U.S.

These are important factors to remember, because these advantages have kept Alliance Resource Partners profitable, while so many other coal companies have gone bankrupt in the past year.

In addition, Alliance Resource Partners is cheap, with a price-earnings ratio of 12, compared with 20 for the S&P 500.

2. Plains All American (PAA - Get Report)
Like many other oil and gas MLPs, Plains All American has been hit hard by the steep drop in oil prices. Over the past two years, oil has sunk from above $100 per barrel to $43 per barrel.

And yet, Plains All American hasn't cut 70-cent-a-share quarterly distribution this year.

The biggest reason for Plains All American's relative stability is that it operates in the midstream space of the oil and gas industry.

Whereas upstream exploration and production firms are entirely reliant on commodity prices, midstream companies aren't. That is because midstream companies own and operate transportation assets such as pipelines and storage terminals.

This is a crucial difference.

Plains All American operates similarly to a toll road. It gets paid fees based on the volumes stored and transported through its asset network.

As long as demand holds steady or increases, as it has in the U.S., then midstream operators can still generate enough cash flow to sustain their distributions.

Plains All American has a very high-quality asset base that fuels its steady cash flow. At the end of last year, the company operated a network of more than 18,000 miles of crude oil and natural-gas liquids pipelines and gathering systems, along with more than 140 transport barges.

In all, Plains All American has storage capacity for 80 million barrels of oil, 25 million barrels of natural-gas liquids storage capacity and another 97 billion cubic feet of natural-gas storage capacity.

During the first half this year, Plains All American generated adjusted earnings before interest, taxes, depreciation and amortization of $1.08 billion. This was a decrease of just 2% from a year earlier.

The company expects to cover its distribution by 1.05 times with distributable cash flow, which is a positive indicator that its 10% yield is sustainable, barring another huge decline in commodity prices.

3. StoneMor Partners (STON - Get Report)
Unlike the vast majority of MLPs, StoneMor Partners has nothing to do with oil and gas. This could be an advantage for investors wary of buying oil and gas MLPs, given the collapse in the energy sector over the past two years.

Instead, StoneMor Partners owns and operates cemeteries in the U.S. and Puerto Rico, and it also sells funeral-related products such as caskets and urns.

What makes StoneMor Partners interesting isn't just its sky-high distribution yield, which stands at 10.6%, but its strong business model. Whereas many industries change rapidly from year to year leaving companies vulnerable to competition, StoneMor Partners operates in a highly stable industry.

After all, death is one of the only certainties in life. The concept of immortality is a popular subject in television and movies, but in reality, there will always be demand for this MLP's products and services.

And, due to population growth and the aging population, StoneMor Partners has a long runway of growth ahead of it.

StoneMor Partners generates significant cash flow from its business model, which it uses to buy more properties, which generate additional cash flow. This results in a snowball effect of sorts, which is why the company can distribute such a high yield to its investors.

For example, the MLP's revenue grew 6% last year and increased 1% in the first half this year. StoneMor Partners, like many other MLPs, reports its distributable cash flow as a non-generally accepted accounting principles equivalent metric to earnings per share.

Distributable cash flow grew 4% last year. The company earned $2.72 in distributable cash flow per unit last year, which covers its annualized distribution of $2.64 a unit.

StoneMor Partners yields 10.7%.

This article is commentary by an independent contributor. At the time of publication, the author held no positions in the stocks mentioned.